A device contains two circuits. The second circuit is a backup for the first, so the second is used only when the first has fail
ed. The device fails when and only when the second circuit fails. Let X and Y be the times (in years) at which the first and second circuits fail, respectively. Their joint probability density function (pdf) is 6e-xe-20 for 0 < x < y 〈 oo; otherwise (a) Find the pdf of X. Identify the distribution of X (b) Find the pdf of Y (c) What is the expected time at which the device fails?
1 answer:
Answer:
Step-by-step explanation:
The pdf of X is given by 3e^x(1-e^-2y). Please check the screenshot for the workings.
The pdf of Y is given by 6e^-2y. Please check the screenshot for the workings.
The expected time the device fails is the expected time Y fails, so we are going to find the expected time of Y which equals to 0.83.
Please check the screenshop for the workings. Thanks
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Answer:
Step-by-step explanation:
I am going to say that:
Mary's amount is x.
Ashley's amount is y.
Oscar's amount is z.
Mary has at least 3 times the amount of cash that ashley and oscar have combined
Ashley's and Oscar's combined amount is y + z.
3 times this amount is 3(y + z).
At least 3 times means that z is equal or greater than 3(y + z).
So